Preheat the oven to 350°F (175°C) and lightly grease a 9-inch pie dish.
Combine graham cracker crumbs, brown sugar, cinnamon, and melted butter. Press the mixture into the bottom and sides of the pie dish.
In a bowl, beat softened cream cheese, sugar, vanilla, and egg until smooth. Spread evenly over the crust.
Toss diced apples with sugar and cinnamon. Distribute evenly over the cheesecake layer.
Combine oats, flour, brown sugar, and cinnamon. Cut in cold butter until crumbly. Sprinkle evenly over the apples.
Bake for 45–50 minutes, or until the topping is golden and the center is set.
Let the pie cool completely, then refrigerate for at least 3 hours before slicing.
Serve chilled or at room temperature with a drizzle of caramel sauce if desired.
